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Chap023 - Chapter 23 Managing Risk off the Balance Sheet...

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Chapter 23 - Managing Risk off the Balance Sheet with Derivative Securities Answers to Chapter 23 Questions 1. The major differences between futures and forward contracts are: i. Futures contracts are traded in open exchanges in standardized units, with fixed maturities. Forward contracts are bilateral agreements between two counter parties. Hence, they can be tailor-made to the buyer = s satisfaction. ii. Futures contracts are marked to market every day while forward contracts are not. Consequently, default risk is higher for the latter. iii. Futures contracts are rarely delivered. Instead, they are closed out (reversed) prior to maturity. Delivery usually takes place for most forward contracts. 2. a. Sell forward b. Buy forward c. Sell forward d. Sell forward e. Sell forward f. Buy forward 3. a. You are obligated to take delivery of a $100,000 face value 20-year Treasury bond at a price of $95,000 at some predetermined later date. b. This is a long hedge, undertaken to protect the FI against falling interest rates. c. You lose $1,000, since you are obliged to pay $95,000 although the current futures price is only $94,000. d. You gain $2,000 since you are obliged to pay $95,000 while the current futures price is $97,000. 4. a. The 20-year 8% coupon $100,000 Treasury bond has a duration of 10.292 years. Time Exponent CF PVIF PVCF PVCF*t 0.5 1 4,000 .9615 3,846.2 1,923.1 1.0 2 4,000 .9246 3,698.2 3,698.2 1.5 3 4,000 .8890 3,556.0 5,334.0 2.0 4 4,000 .8548 3,419.2 6,838.4 2.5 5 4,000 .8219 3,287.7 8,219.3 3.0 6 4,000 .7903 3,161.3 9,483.8 3.5 7 4,000 .7599 3,039.7 10,639.0 4.0 8 4,000 .7307 2,922.8 11,691.0 4.5 9 4,000 .7026 2,810.3 12,647.0 5.0 10 4,000 .6756 2,702.3 13,511.0 5.5 11 4,000 .6496 2,598.3 14,291.0 6.0 12 4,000 .6246 2,498.4 14,990.0 6.5 13 4,000 .6006 2,402.3 15,615.0 7.0 14 4,000 .5775 2,309.9 16,169.0 7.5 15 4,000 .5553 2,221.1 16,658.0 8.0 16 4,000 .5339 2,135.6 17,085.0 23-1
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Chapter 23 - Managing Risk off the Balance Sheet with Derivative Securities 8.5 17 4,000 .5134 2,053.5 17,455.0 9.0 18 4,000 .4936 1,974.5 17,771.0 9.5 19 4,000 .4746 1,898.6 18,036.0 10.0 20 4,000 .4564 1,825.5 18,255.0 10.5 21 4,000 .4388 1,755.3 18,431.0 11.0 22 4,000 .4220 1,687.8 18,566.0 11.5 23 4,000 .4075 1,622.9 18,663.0 12.0 24 4,000 .3901 1,560.5 18,726.0 12.5 25 4,000 .3751 1,500.5 18,756.0 13.0 26 4,000 .3607 1,442.8 18,756.0 13.5 27 4,000 .3468 1,387.3 18,728.0 14.0 28 4,000 .3335 1,333.9 18,675.0 14.5 29 4,000 .3207 1,282.6 18,598.0 15.0 30 4,000 .3083 1,233.3 18,499.0 15.5 31 4,000 .2965 1,185.8 18,381.0 16.0 32 4,000 .2851 1,140.2 18,244.0 16.5 33 4,000 .2741 1,096.4 18,990.0 17.0 34 4,000 .2636 1,054.2 17,922.0 17.5 35 4,000 .2534 1,013.7 17,739.0 18.0 36 4,000 .2437 974.7 17,544.0 18.5 37 4,000 .2343 937.2 17,338.0 19.0 38 4,000 .2253 901.1 17,122.0 19.5 39 4,000 .2166 866.5 16,896.0 20.0 40 104,000 .2083 21,662.0 433,240.0 Sum 100,000.00 1,029,200 Duration = 1,029,200/100,000 = 10.292 b. ΔP/P = -D(ΔR/(1 + R)) Ψ ΔP = -D(ΔR/(1 + R))P = -10.292(0.0025/(1 + 0.04))$100,000 = -2,474.04 The price decline of the $100,000 Treasury bond is $2,474.04 c. A bid-ask quote of 101 - 13 = $101 13/32 per $100 face value. Since the Treasury bond futures contracts are for $100,000 face value, the quoted price is $101,406.25. 5. The expected change in the spot position = -9.4 Η (.01/1.07) Η 10,400,000 = -$913,645. This would mean a price change from 104 to 94.86355 per $100 face value. By entering into a two month forward contract to sell a $10,000,000 of 15 year bonds at 104, the FI will have hedged its spot position. If rates rise by 1% and the bond value falls by $913,645, the FI can close out its forward position by receiving 104 for bonds worth 94.86355. The profit on the forward position will offset the loss in the spot market. 23-2
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Chapter 23 - Managing Risk off the Balance Sheet with Derivative Securities 6. a. The FI can either (i) buy a call option, or (ii) sell a put option on interest rate instruments, such as T-bonds, to generate positive cash flows in the event that interest rates decline.
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